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| unit frmPostfix;
interface
uses
Windows, SysUtils, Classes, Controls, Forms, Contnrs, StdCtrls, Math;
type
POperation = ^TOperation;
TOperation = packed record
Name: string;
OpCount: Byte;
Priority: Byte;
end;
PSymbol = ^TSymbol;
TSymbol = packed record
Kind: (tkNumber, tkOperation, tkOpenedBracket, tkClosedBracket);
case Byte of
0: (Number: Double);
1: (Operation: DWORD);
end;
TExpression = array of TSymbol;
TPostfixFrm = class(TForm)
ExpEdt: TEdit;
ParsedEdt: TEdit;
ParseBtn: TButton;
ResultEdt: TEdit;
EvalBtn: TButton;
procedure ParseBtnClick(Sender: TObject);
procedure EvalBtnClick(Sender: TObject);
private
{ Private declarations }
ConvExp: TExpression;
{ *** }
function OpIndexToPtr(const OpIndex: DWORD): POperation;
function ExprToStr(const Expr: TExpression): string;
{ *** }
function ParseExpression(Expression: string;
var ParsedExp: TExpression): Boolean;
function ConvertExpression(const ParsedExp: TExpression;
var ConvertedExp: TExpression): Boolean;
function EvaluateExpression(const ConvertedExp: TExpression;
var aResult: Double): Boolean;
public
{ Public declarations }
end;
const
OPERATION_COUNT = 15;
Operations: array [0..OPERATION_COUNT-1] of TOperation =
{ Name: <имя_операции>; OpCount: <колво_операндов>; Priority: <приоритет>;
(нулевой приоритет использовать НИЗЗЗЗЯЯЯ!!!!) }
((Name:'+'; OpCount:2; Priority:1),
(Name:'-'; OpCount:2; Priority:1),
(Name:'*'; OpCount:2; Priority:2),
(Name:'/'; OpCount:2; Priority:2),
(Name:'^'; OpCount:2; Priority:4),
(Name:'sin'; OpCount:1; Priority:255),
(Name:'cos'; OpCount:1; Priority:255),
(Name:'arcsin'; OpCount:1; Priority:255),
(Name:'arccos'; OpCount:1; Priority:255),
(Name:'ln'; OpCount:1; Priority:255),
(Name:'exp'; OpCount:1; Priority:255),
(Name:'round'; OpCount:1; Priority:255),
(Name:'trunc'; OpCount:1; Priority:255),
(Name:'tan'; OpCount:1; Priority:255),
(Name:'cotan'; OpCount:1; Priority:255));
var
PostfixFrm: TPostfixFrm;
implementation
{$R *.dfm}
{ TPostfixFrm }
function TPostfixFrm.OpIndexToPtr(const OpIndex: DWORD): POperation;
begin
Result := @Operations[OpIndex];
end;
function TPostfixFrm.ExprToStr(const Expr: TExpression): string;
var
i: Integer;
begin
Result := '';
for i := 0 to High(Expr) do
case Expr[i].Kind of
tkNumber: Result := Result + FloatToStr(Expr[i].Number) + ' ';
tkOperation: Result := Result + OpIndexToPtr(Expr[i].Operation).Name + ' ';
tkOpenedBracket: Result := Result + '( ';
tkClosedBracket: Result := Result + ') ';
end;
end;
function TPostfixFrm.ParseExpression(Expression: string;
var ParsedExp: TExpression): Boolean;
function FindOp(const sym: string): Integer;
var
i: Integer;
begin
Result := -1;
for i := 0 to OPERATION_COUNT-1 do
if sym = Operations[i].Name then
begin
Result := i;
Exit;
end;
end;
function AddSymbol(const sym: string): Boolean;
var
f: Extended;
IsNumber: Boolean;
op: Integer;
begin
Result := True; if (sym = '') or (sym[1] = #0) then Exit;
SetLength(ParsedExp,Length(ParsedExp)+1);
if sym = '(' then
begin
ParsedExp[High(ParsedExp)].Kind := tkOpenedBracket;
Exit;
end;
if sym = ')' then
begin
ParsedExp[High(ParsedExp)].Kind := tkClosedBracket;
Exit;
end;
IsNumber := TextToFloat(PChar(sym),f,fvExtended);
if IsNumber then
begin
ParsedExp[High(ParsedExp)].Kind := tkNumber;
ParsedExp[High(ParsedExp)].Number := f;
end else
begin
ParsedExp[High(ParsedExp)].Kind := tkOperation;
op := FindOp(sym);
if op = -1 then
begin
Result := False;
Exit;
end;
ParsedExp[High(ParsedExp)].Operation := op;
end;
end;
const
Separators = ['+','-','/','*','(',')','^'];
var
i: Integer;
s: string;
begin
Result := False; Finalize(ParsedExp);
i := 0;
while i <> Length(Expression) do
if Expression[i] = ' ' then Delete(Expression,i,1) else Inc(i);
Expression := '('+Expression+')';
i := Pos('(-',Expression);
while i > 0 do
begin
Insert('0',Expression,i+1);
i := Pos('(-',Expression);
end;
for i := 1 to Length(Expression) do
if Expression[i] in Separators then
begin
if not AddSymbol(s) then Exit;
if not AddSymbol(Expression[i]) then Exit;
s := '';
end else
s := s + Expression[i];
Result := True;
end;
function TPostfixFrm.ConvertExpression(const ParsedExp: TExpression;
var ConvertedExp: TExpression): Boolean;
procedure CopySymbol(const sym: PSymbol);
begin
SetLength(ConvertedExp,Length(ConvertedExp)+1);
ConvertedExp[High(ConvertedExp)] := sym^;
end;
var
i: Integer;
psym: PSymbol;
OldPrior: Byte;
Stack: TStack;
begin
Finalize(ConvExp); Result := True; i := -1;
Stack := TStack.Create;
try
while i < High(ParsedExp) do
begin
Inc(i); OldPrior := 0;
if (Stack.Count > 0) and (PSymbol(Stack.Peek).Kind = tkOperation) then
OldPrior := OpIndexToPtr(PSymbol(Stack.Peek).Operation).Priority;
case ParsedExp[i].Kind of
tkNumber: CopySymbol(@ParsedExp[i]);
tkOperation:
if (OldPrior >= OpIndexToPtr(ParsedExp[i].Operation).Priority) then
begin
CopySymbol(Stack.Pop);
Dec(i);
end else Stack.Push(@ParsedExp[i]);
tkOpenedBracket: Stack.Push(@ParsedExp[i]);
tkClosedBracket:
begin
if Stack.Count = 0 then
begin
Result := False;
Break;
end;
psym := Stack.Pop;
if psym.Kind <> tkOpenedBracket then
begin
CopySymbol(psym);
Dec(i);
end else
if (Stack.Count > 0) and (PSymbol(Stack.Peek).Kind = tkOperation) and
(OpIndexToPtr(PSymbol(Stack.Peek).Operation).Priority = 255) then
CopySymbol(Stack.Pop);
end;
end;
end;
while Stack.Count > 0 do CopySymbol(Stack.Pop);
finally
Stack.Free;
end;
end;
function TPostfixFrm.EvaluateExpression(const ConvertedExp: TExpression;
var aResult: Double): Boolean;
function ExecOp(OpIndex: Byte; Operands: array of Double): Double;
begin
case OpIndex of
0: Result := Operands[1] + Operands[0]; { сумма }
1: Result := Operands[1] - Operands[0]; { разность }
2: Result := Operands[1] * Operands[0]; { произведение }
3: Result := Operands[1] / Operands[0]; { деление }
4: Result := Power(Operands[1],Operands[0]); { степень }
5: Result := sin(Operands[0]);
6: Result := cos(Operands[0]);
7: Result := arcsin(Operands[0]);
8: Result := arccos(Operands[0]);
9: Result := ln(Operands[0]);
10: Result := exp(Operands[0]);
11: Result := round(Operands[0]);
12: Result := trunc(Operands[0]);
13: Result := tan(Operands[0]);
14: Result := cotan(Operands[0]);
else Result := 0;
end;
end;
var
i,j: Integer;
Stack: TStack;
TmpNums: array of PSymbol;
Ops: array of Double;
begin
Result := True; Stack := TStack.Create;
try
for i := 0 to High(ConvertedExp) do
begin
if ConvertedExp[i].Kind = tkNumber then Stack.Push(@ConvertedExp[i]) else
begin
if (ConvertedExp[i].Kind in [tkOpenedBracket,tkClosedBracket]) or
(Stack.Count < OpIndexToPtr(ConvertedExp[i].Operation).OpCount) then
begin
Result := False;
Break;
end;
SetLength(Ops,OpIndexToPtr(ConvertedExp[i].Operation).OpCount);
for j := 0 to High(Ops) do
Ops[j] := PSymbol(Stack.Pop).Number;
SetLength(TmpNums,Length(TmpNums)+1);
TmpNums[High(TmpNums)] := New(PSymbol);
TmpNums[High(TmpNums)].Kind := tkNumber;
TmpNums[High(TmpNums)].Number :=
ExecOp(ConvertedExp[i].Operation,Ops);
Stack.Push(TmpNums[High(TmpNums)]);
end;
end;
if (Stack.Count = 1) and Result then
aResult := PSymbol(Stack.Pop).Number else Result := False;
finally
Stack.Free;
end;
for i := 0 to High(TmpNums) do Dispose(TmpNums[i]);
end;
procedure TPostfixFrm.ParseBtnClick(Sender: TObject);
var
ParsedExpression: TExpression;
begin
ResultEdt.Text := ''; ParsedEdt.Text := ''; EvalBtn.Enabled := False;
if (ParseExpression(ExpEdt.Text,ParsedExpression) and
ConvertExpression(ParsedExpression,ConvExp)) then
begin
ParsedEdt.Text := ExprToStr(ConvExp);
EvalBtn.Enabled := True;
end else
MessageBox(Handle,'Ошибка преобразования выражения!',nil,MB_ICONERROR);
end;
procedure TPostfixFrm.EvalBtnClick(Sender: TObject);
var
rslt: Double;
begin
if EvaluateExpression(ConvExp,rslt) then
ResultEdt.Text := FloatToStr(rslt)
else
MessageBox(Handle,'Ошибка вычисления выражения!',nil,MB_ICONERROR);
end;
end. |